Question

Find the cube root of $64$ by prime factorization method

Answer 1

Finding the cube root of $64$ by Prime Factorization:

Prime factor of $64=2\times 2\times 2\times 2\times 2\times 2$
$$\begin{gathered} =2^3\times 2^3 \\ ={(2\times 2)}^3 \\ ={\left(4\right)}^3 \end{gathered}$$
$$\begin{gathered} \therefore \sqrt[3]{64}=\sqrt[3]{{\left(4\right)}^3} \\ ={\left(4^3\right)}^{\frac{1}{3}} \\ =4\mathbf{}\left[\because {\left(a^n\right)}^m=a^{\mathrm{nm}}\right] \end{gathered}$$

Hence the cube root of $64$ is $4$